Stay ahead of learning milestones! Enroll in a class over the summer!

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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
May 1, 2025
0 replies
f(f(x+y)) = f(x)+f(y)
NamelyOrange   2
N 5 minutes ago by youochange
Source: Evan's FE handout
Find all continuous $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $f(f(x+y)) = f(x)+f(y)$ for all real $x,y$.
2 replies
NamelyOrange
Mar 14, 2025
youochange
5 minutes ago
Finding Max!
goldeneagle   4
N an hour ago by aidan0626
Source: Iran 3rd round 2013 - Algebra Exam - Problem 2
Real numbers $a_1 , a_2 , \dots, a_n$ add up to zero. Find the maximum of $a_1 x_1 + a_2 x_2 + \dots + a_n x_n$ in term of $a_i$'s, when $x_i$'s vary in real numbers such that $(x_1 - x_2)^2 + (x_2 - x_3)^2 + \dots + (x_{n-1} - x_n)^2 \leq 1$.
(15 points)
4 replies
goldeneagle
Sep 11, 2013
aidan0626
an hour ago
Inequalities
produit   0
an hour ago
Find the lowest value of C for which there exists such sequence
1 = x_0 ⩾ x_1 ⩾ x_2 ⩾ . . . ⩾ x_n ⩾ . . .
that for any positive integer n
x_{0}^2/x_{1}+x_{1}^{2}/x_{2}+ . . . +x_{n}^2/x_{n+1}< C.
0 replies
1 viewing
produit
an hour ago
0 replies
Easy Number Theory
math_comb01   38
N 2 hours ago by lakshya2009
Source: INMO 2024/3
Let $p$ be an odd prime and $a,b,c$ be integers so that the integers $$a^{2023}+b^{2023},\quad b^{2024}+c^{2024},\quad a^{2025}+c^{2025}$$are divisible by $p$.
Prove that $p$ divides each of $a,b,c$.
$\quad$
Proposed by Navilarekallu Tejaswi
38 replies
math_comb01
Jan 21, 2024
lakshya2009
2 hours ago
No more topics!
Set of rectangles - [IMO LongList 1971]
Amir Hossein   1
N Jan 2, 2011 by oneplusone
An infinite set of rectangles in the Cartesian coordinate plane is given. The vertices of each of these rectangles have coordinates $(0, 0), (p, 0), (p, q), (0, q)$ for some positive integers $p, q$. Show that there must exist two among them one of which is entirely contained in the other.
1 reply
Amir Hossein
Jan 1, 2011
oneplusone
Jan 2, 2011
Set of rectangles - [IMO LongList 1971]
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Amir Hossein
5452 posts
#1 • 2 Y
Y by Adventure10, Mango247
An infinite set of rectangles in the Cartesian coordinate plane is given. The vertices of each of these rectangles have coordinates $(0, 0), (p, 0), (p, q), (0, q)$ for some positive integers $p, q$. Show that there must exist two among them one of which is entirely contained in the other.
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oneplusone
1459 posts
#2 • 2 Y
Y by Adventure10, Mango247
Consider the rectangle $R$ with the vertex $(p_0,q_0)$. If 2 rectangles has the same $p$ or $q$ value, then one must be contained in another. Then there are at most $p_0+q_0-2$ other rectangles whose $p$ or $q$ value is less than $p_0$ or $q_0$ respectively. All the other rectangles will have $p,q$ value more than $p_0,q_0$, so they all contain $R$.
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